Mathematical Libraries as Proof Assistant Environments Claudio Sacerdoti Coen ⋆ Department of Computer Science University of Bologna Mura Anteo Zamboni 7, 40127 Bologna, ITALY sacerdot@cs.unibo.it Abstract. In this paper we analyse the modifications on logical oper- ations — as proof checking, type inference, reduction and convertibility — that are required for the identification of a proof assistant environ- ment with a distributed mathematical library, focusing on proof assis- tants based on the Curry-Howard isomorphism. This identification is aimed at the integration of Mathematical Knowl- edge Management tools with interactive theorem provers: once the dis- tinction between the proof assistant environment and a mathematical library is blurred, it is possible to exploit Mathematical Knowledge Man- agement rendering, indexing and searching services inside an interactive theorem prover, a first step towards effective loosely-coupled collabora- tive mathematical environments. 1 Introduction The main goal of Mathematical Knowledge Management (MKM) is the creation of large distributed libraries of mathematical knowledge and the development of tools to manage, render, data mine, index and retrieve the notions in these libraries. Mathematical Knowledge Management does not study the process of new mathematical knowledge creation by a mathematician, but is expected to have a substantial impact on it: the better the existent knowledge is grasped and retrieved, the quicker the process of creation. For instance, recent studies [2,3] implement an authomatic knowledge discovery framework by tightly integrating Mathematical Knowledge Management with authomatic theorem proving: the existent mathematical knowledge is used to derive new definitions, to guess in- teresting properties and to drive the theorem prover by suggesting well known proof techniques; the theorem prover is used to detect the properties that hold and prune out wrong guesses. It is not known whether all the expectations will be met or whether the mathematicians will not adopt the Mathematical Knowledge Management tools finding them useless. Nevertheless, we already have evidence of the necessity for ⋆ Partially supported by ‘MoWGLI: Math on the Web, Get it by Logic and Interfaces’, EU IST-2001-33562